Table of contents
About this tutorial
4
Introduction to single-phase power 6
1 DC power
8
1.1 Basic DC power
8
2 Single-phase AC power
10
2.1 Single-phase power with resistive loads
2.1.1 Resistive loads—basic AC power
2.1.2 Resistive loads—RMS values and why we use them 2.1.3 Resistive loads—RMS voltages
2.1.4 Resistive loads—RMS voltage properties 2.1.5 Resistive loads—voltage and current in phase 2.2 Single-phase power with inductive loads
2.2.1 Inductive loads—introducing phase shift 2.2.2 Inductive loads—voltage, current and power 2.2.3 Inductive loads—separating instantaneous into active and reactive power
2.2.4 Inductive loads—active, reactive and apparent power 2.2.5 Inductive loads—apparent power and the canal boat metaphor
2.2.6 Inductive loads—power factor
2.3 Single-phase power with inductive loads and harmonic distortion
2.3.1 Harmonic distortion—going beyond Classical theory
2.3.2 Harmonic distortion—simplified by Fourier analysis
2.3.3 Harmonic distortion—voltage, current and power 2.3.4 Harmonic distortion—active, reactive and apparent power
2.3.5 Harmonic distortion—where does it come from?
2.3.6 Harmonic distortion—why is S2 no longer just P2 + Q2? 2.3.7 Harmonic distortion—a summary of calculations 2.3.8 Harmonic distortion—performance parameters
2.4 Single-phase power summary
2.4.1 Summary—example parameter values
2.4.2 Summary—single-phase power formulae
2.4.3 Summary—single-phase power parameters Introduction to three-phase power 41
3 Three-phase AC power 42
3.1 Three-phase symbols and colors
3.2 Three-phase balanced sine-wave systems
3.2.1 Balanced sine-wave—basic system
3.2.2 Balanced sine-wave—voltage and current waveforms
3.2.3 Balanced sine-wave – vector diagram 3.2.4 Balanced sine-wave—positive sequence
3.2.5 Balanced sine-wave—negative sequence 3.2.6 Balanced sine-wave—positive- and negative-sequence waveforms 3.2.7 Balanced sine-wave—phase and system-level parameters 3.2.8 Balanced sine-wave—phase and system-level powers
3.2.9 Balanced sine-wave—voltage, current and power overview
3.3 Wye and delta configuration
3.3.1 Wye and delta—basic circuits
3.3.2 Wye and delta—vector diagram
3.3.3 Wye and delta—a summary of differences
3.3.4 Wye and delta—power in delta systems with two-wattmeter method
3.3.5 Wye and delta—delta powers and power factor
3.4 Three-phase unbalanced sine-wave systems
3.4.1 Unbalanced sine-wave—unbalanced currents from inductive loads
2 Fluke Corporation
10
10
11
13
14
15
16
16
18
19
21
23
25
26
26
27
28
29
31
33
34
35
36
36
38
39
Electrical power explained
42
43
43
44
45
46
47
48
49
50
51
52
52
53
54
55
56
58
58
3.4.2 Unbalanced sine-wave—apparent power vector diagram
59
3.4.3 Unbalanced sine-wave—apparent power calculation methods
60
3.4.4 Unbalanced sine-wave—apparent power the Classical way (Sa and Sv)62
3.4.5 Unbalanced sine-wave—apparent power the IEEE 1459 way (Se and Se1)63
3.4.6 Unbalanced sine-wave—apparent power the Unified way (S and S1)64
3.5 Symmetrical components
65
3.5.1 Symmetrical components—introduction 65
3.5.2 Symmetrical components—vector view
66
3.5.3 Symmetrical components—introducing symmetrical powers 67
3.5.4 Symmetrical components—current waveforms
68
3.5.5 Symmetrical components—the symmetrical transformation
69
3.5.6 Symmetrical components—the transformed current waveforms
70
3.5.7 Symmetrical components—checking the currents
72
3.5.8 Symmetrical components—active and reactive positive-sequence currents
73
3.5.9 Symmetrical components—a summary of the powers
74
3.6 Unbalance sine-wave examples
76
3.6.1 Unbalance examples—resistive load with three lamps 76
3.6.2 Unbalance examples—effects of a burned-out lamp
77
3.6.3 Unbalance examples—effects of poor installation
79
3.6.4 Unbalance examples—effects of extremely poor installation
80
3.7 Combined three-phase power (unbalance and harmonics)
81
3.7.1 Combined power—unbalance and harmonic distortion
81
3.7.2 Combined power—how the powers all fit together 82
3.7.3 Combined power—example with unbalance and harmonic distortion
83
3.7.4 Combined power—unbalance vector diagram 84
3.7.5 Combined power—example with unbalance and harmonics
85
3.7.6 Combined power—example with unbalance and harmonics (contd.)
87
3.8 Neutral currents
88
3.8.1 Neutral currents—due to unbalance
88
3.8.2 Neutral currents—due to harmonics
89
3.8.3 Neutral currents—due to harmonics and unbalance
90
3.9 Power summaries
92
3.9.1 Power summaries­— Classical parameters
92
3.9.2 Power summaries—Unified parameters
93
3.9.3 Power summaries—IEEE 1459 parameters
94
3.9.4 Power summaries—power directions
95
Introduction to power loss 97
4 Power loss 98
4.1 Single-phase power loss
4.2 Three-phase power loss
4.2.1 Three-phase loss—line power loss in practice
4.2.2 Three-phase loss—line power loss from a user perspective
4.2.3 Three-phase loss—calculating losses by decomposing line current 4.2.4 Three-phase loss—line current components
4.2.5 Three-phase loss—finding or estimating line resistance
4.2.6 Three-phase loss—calculating line power loss
4.2.7 Three-phase losses—a real-world line power loss example
5 Appendix
5.1 IEEE 1459 and Unified apparent power compared
5.2 Unified apparent power components
98
100
100
101
102
104
105
106
107
109
109
111
6 Electrical timeline
115
7 References
117
Electrical power explained
Fluke Corporation 3